Average Error: 6.0 → 0.8
Time: 2.9s
Precision: 64
\[x + \frac{y \cdot \left(z - t\right)}{a}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.2868591936461545 \cdot 10^{87} \lor \neg \left(y \cdot \left(z - t\right) \le 2.6367459781683227 \cdot 10^{296}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]
x + \frac{y \cdot \left(z - t\right)}{a}
↓
\begin{array}{l}
\mathbf{if}\;y \cdot \left(z - t\right) \le -5.2868591936461545 \cdot 10^{87} \lor \neg \left(y \cdot \left(z - t\right) \le 2.6367459781683227 \cdot 10^{296}\right):\\
\;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\

\end{array}
double code(double x, double y, double z, double t, double a) {
	return (x + ((y * (z - t)) / a));
}
↓
double code(double x, double y, double z, double t, double a) {
	double VAR;
	if ((((y * (z - t)) <= -5.2868591936461545e+87) || !((y * (z - t)) <= 2.6367459781683227e+296))) {
		VAR = fma((y / a), (z - t), x);
	} else {
		VAR = (x + ((y * (z - t)) / a));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.0
Target0.8
Herbie0.8
\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* y (- z t)) < -5.2868591936461545e+87 or 2.6367459781683227e+296 < (* y (- z t))

    1. Initial program 23.4

      \[x + \frac{y \cdot \left(z - t\right)}{a}\]

    2. Simplified1.8

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)}\]

    if -5.2868591936461545e+87 < (* y (- z t)) < 2.6367459781683227e+296

    1. Initial program 0.4

      \[x + \frac{y \cdot \left(z - t\right)}{a}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.2868591936461545 \cdot 10^{87} \lor \neg \left(y \cdot \left(z - t\right) \le 2.6367459781683227 \cdot 10^{296}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020102 +o rules:numerics
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

  (+ x (/ (* y (- z t)) a)))